Improved Stability and Stabilization Results for Stochastic Synchronization of Continuous-Time Semi-Markovian Jump Neural Networks With Time-Varying Delay

Continuous-time semi-Markovian jump neural networks (semi-MJNNs) are those MJNNs whose transition rates are not constant but depend on the random sojourn time. Addressing stochastic synchronization of semi-MJNNs with time-varying delay, an improved stochastic stability criterion is derived in this paper to guarantee stochastic synchronization of the response systems with the drive systems. This is achieved through constructing a semi-Markovian Lyapunov–Krasovskii functional together as well as making use of a novel integral inequality and the characteristics of cumulative distribution functions. Then, with a linearization procedure, controller synthesis is carried out for stochastic synchronization of the drive-response systems. The desired state-feedback controller gains can be determined by solving a linear matrix inequality-based optimization problem. Simulation studies are carried out to demonstrate the effectiveness and less conservatism of the presented approach.

[1]  Min Wu,et al.  Free-Matrix-Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay , 2015, IEEE Transactions on Automatic Control.

[2]  Min Wu,et al.  Delay-Dependent Stability Criteria for Generalized Neural Networks With Two Delay Components , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[3]  Yohann Foucher,et al.  A Semi‐Markov Model Based on Generalized Weibull Distribution with an Illustration for HIV Disease , 2005, Biometrical journal. Biometrische Zeitschrift.

[4]  Z. Duan,et al.  Synchronization transitions on scale-free neuronal networks due to finite information transmission delays. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Xinsong Yang,et al.  Finite-Time Synchronization of Coupled Networks With Markovian Topology and Impulsive Effects , 2016, IEEE Transactions on Automatic Control.

[6]  Guanrong Chen,et al.  Synchronization transitions on small-world neuronal networks: Effects of information transmission delay and rewiring probability , 2008 .

[7]  Xin-Ping Guan,et al.  Decentralized Output Feedback Adaptive NN Tracking Control for Time-Delay Stochastic Nonlinear Systems With Prescribed Performance , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[8]  Jinde Cao,et al.  Exponential H∞ filtering analysis for discrete-time switched neural networks with random delays using sojourn probabilities , 2016, Science China Technological Sciences.

[9]  Yan Gao,et al.  Mode and Delay-Dependent Adaptive Exponential Synchronization in $p$th Moment for Stochastic Delayed Neural Networks With Markovian Switching , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[10]  Peng Shi,et al.  Mixed H-Infinity and Passive Filtering for Discrete Fuzzy Neural Networks With Stochastic Jumps and Time Delays , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[11]  Jinde Cao,et al.  Necessary and sufficient condition for the absolute exponential stability of a class of neural networks with finite delay , 2006 .

[12]  Shengyuan Xu,et al.  Stability Analysis of Distributed Delay Neural Networks Based on Relaxed Lyapunov–Krasovskii Functionals , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[13]  Bing Chen,et al.  Robust Stability for Uncertain Delayed Fuzzy Hopfield Neural Networks With Markovian Jumping Parameters , 2009, IEEE Trans. Syst. Man Cybern. Part B.

[14]  Jinde Cao,et al.  Fixed-time synchronization of delayed memristor-based recurrent neural networks , 2017, Science China Information Sciences.

[15]  Ting Wang,et al.  Combined Convex Technique on Delay-Dependent Stability for Delayed Neural Networks , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[16]  Guanrong Chen,et al.  Synchronous Bursts on Scale-Free Neuronal Networks with Attractive and Repulsive Coupling , 2010, PloS one.

[17]  Jinde Cao,et al.  Exponential Synchronization of Coupled Stochastic Memristor-Based Neural Networks With Time-Varying Probabilistic Delay Coupling and Impulsive Delay , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[18]  Xin-Ping Guan,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Time-Varying Delay Using Delay-Decomposition Approach , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[19]  M. Perc,et al.  Gap Junctions and Epileptic Seizures – Two Sides of the Same Coin? , 2011, PloS one.

[20]  Hamid Reza Karimi,et al.  Filtering design for two-dimensional Markovian jump systems with state-delays and deficient mode information , 2014, Inf. Sci..

[21]  Yong He,et al.  Global exponential stability of neural networks with time-varying delay based on free-matrix-based integral inequality , 2016, Neural Networks.

[22]  Huijun Gao,et al.  New Delay-Dependent Exponential H ∞ Synchronization for Uncertain Neural Networks With Mixed Time Delays , 2009 .

[23]  Jinde Cao,et al.  Finite-time boundedness, L2-gain analysis and control of Markovian jump switched neural networks with additive time-varying delays , 2017 .

[24]  Engang Tian,et al.  Improved global robust delay-dependent stability criteria for delayed cellular neural networks , 2008, Int. J. Comput. Math..

[25]  M. Perc,et al.  Complex synchronous behavior in interneuronal networks with delayed inhibitory and fast electrical synapses. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Yonggui Kao,et al.  A sliding mode approach to robust stabilisation of Markovian jump linear time-delay systems with generally incomplete transition rates , 2015 .

[27]  Yang Shi,et al.  Stochastic stability and robust stabilization of semi‐Markov jump linear systems , 2013 .

[28]  Yong He,et al.  Stability Analysis for Delayed Neural Networks Considering Both Conservativeness and Complexity , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[29]  Xin-Ping Guan,et al.  Synchronization of Chaotic Lur’e Systems With Time Delays Using Sampled-Data Control , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[30]  Yonggui Kao,et al.  A sliding mode approach to H∞ non-fragile observer-based control design for uncertain Markovian neutral-type stochastic systems , 2015, Autom..

[31]  James Lam,et al.  Stability and Synchronization of Discrete-Time Neural Networks With Switching Parameters and Time-Varying Delays , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[32]  Y. Wang,et al.  Stability Analysis of Markovian Jumping Stochastic Cohen–Grossberg Neural Networks With Mixed Time Delays , 2008, IEEE Transactions on Neural Networks.

[33]  Kumpati S. Narendra,et al.  Identification and control of dynamical systems using neural networks , 1990, IEEE Trans. Neural Networks.

[34]  Wenwu Yu,et al.  Synchronization on Complex Networks of Networks , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[35]  Tae H. Lee,et al.  Stochastic sampled-data control for state estimation of time-varying delayed neural networks , 2013, Neural Networks.

[36]  Jinde Cao,et al.  Synchronization of Neural Networks With Control Packet Loss and Time-Varying Delay via Stochastic Sampled-Data Controller , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[37]  Frédéric Gouaisbaut,et al.  Wirtinger-based integral inequality: Application to time-delay systems , 2013, Autom..

[38]  Guanrong Chen,et al.  Impact of delays and rewiring on the dynamics of small-world neuronal networks with two types of coupling , 2010 .

[39]  Dong Yue,et al.  Delay-Distribution-Dependent Exponential Stability Criteria for Discrete-Time Recurrent Neural Networks With Stochastic Delay , 2008, IEEE Transactions on Neural Networks.

[40]  Jia Wang,et al.  Event-Triggered Generalized Dissipativity Filtering for Neural Networks With Time-Varying Delays , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[41]  Huaguang Zhang,et al.  Networked Synchronization Control of Coupled Dynamic Networks With Time-Varying Delay , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[42]  Hamid Reza Karimi,et al.  Stability of Markovian Jump Generalized Neural Networks With Interval Time-Varying Delays , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[43]  Hamid Reza Karimi,et al.  Robust Delay-Dependent $H_{\infty}$ Control of Uncertain Time-Delay Systems With Mixed Neutral, Discrete, and Distributed Time-Delays and Markovian Switching Parameters , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[44]  Peng Shi,et al.  Stochastic Synchronization of Markovian Jump Neural Networks With Time-Varying Delay Using Sampled Data , 2013, IEEE Transactions on Cybernetics.

[45]  Tieshan Li,et al.  Output-Feedback Adaptive Neural Control for Stochastic Nonlinear Time-Varying Delay Systems With Unknown Control Directions , 2015, IEEE Transactions on Neural Networks and Learning Systems.